Regions between curves

1. The problem statement, all variables and given/known data
Find the region bounded by y= 2x and y = x^2 + 3x - 6.
I found the points of intersection to be x= -3, 2 by setting the equations equal to each other and solving for x.
I concluded that y = x^2+3x-6 is bigger since I tried a point in between the points of intersection and it came out to be greater.

2. Relevant equations
y =2x
y= x^2+3x-6
x= -3, 2

3. The attempt at a solution
I tried integrating x^2+3x-6 dx from -3 to 2. But it doesn't work. What am I doing wrong?
I also tried separating the integrals and integrating from -3 to 0, and from 0 to 2, but doesn't seem to work either. The back of my book says that the answer should be 81/32 but I don't know how they got there. Help!
Thanks!

1. The problem statement, all variables and given/known data
Find the region bounded by y= 2x and y = x^2 + 3x - 6.
I found the points of intersection to be x= -3, 2 by setting the equations equal to each other and solving for x.
I concluded that y = x^2+3x-6 is bigger since I tried a point in between the points of intersection and it came out to be greater.